The match is a tie if both players win as black or if they both win as white.
Probability for this to happen is
60% * 60% + 40% * 40% = 52%.

To get a winner of the match, white must win in one game and black
in the other or reverse. Probability for this to happen is
60% * 40% + 40% * 60% = 48%.

So the outcome (tie or winner) of a two games match of Copenhagen with two equally strong players is like flipping a coin.

If a winner must be found, as fx. in the world championship tournament, a series of matches until one wins will most likely not be long:
The probability of one tie is 52%.
The probability of two ties in a row is 52% * 52% = 27%.
The probability of three ties in a row is 52% * 52% * 52% = 14%.
Etc.

Hagbard wrote:
So the outcome (tie or winner) of a two games match of Copenhagen with two equally strong players is like flipping a coin.

If a winner must be found, as fx. in the world championship tournament, a series of matches until one wins will most likely not be long:
The probability of one tie is 52%.
The probability of two ties in a row is 52% * 52% = 27%.
The probability of three ties in a row is 52% * 52% * 52% = 14%.
Etc.

This is a very interesting statistic. I would prefer this method of tiebreaker (opponents playing two additional games), opposed to tiebreakers like game length or pieces captured. Or as I previously suggested, if players split games in consecutive rounds, each winning a game as black and a game as white, then I think the third round tiebreaker should only be one game to decide the winner. Which player plays which color should be decided randomly, either by a coin flip or a hat pull, by the umpire. In the event of a tie in the fifth game, players would switch colors and continue playing until a winner is found.

If players split games in two consecutive rounds (the round robin round and the addition tiebreaker round, no previous rounds), winning all games as either black or white, then perhaps we could use tiebreakers of game length or pieces captured to determine a winner. Although I am opposed to such tiebreakers, I understand this is the real world and players can potentially continue to split games. So, such tiebreakers is could at least be a means to find a winner. Anyways, the need for an extra tiebreaker round has been rare to this point. I think for sure we should not go past a third round to determine a tournament champion. Depending on the players playing pace, the games could potentially last for months.

This is all just food for thought moving forward. I don’t know what’s the best tiebreaker method. I just prefer playing games not having to worry about game length, pieces captured, or if you lost a game to a weak or strong opponent.

Probability of tie in a match of two tafl games as consequence of game balance.

Game balance 1.00 (perfect) means probability of
white win: 50%
black win: 50%
The match is a tie if both players win as black or if they both win as white. Probability for this to happen is
50% * 50% + 50% * 50% = 50.0%

The game balance where the perfect ratio 1 deviates by 10% and becomes ratio 1.10 is reached atgame balance 1.56

This matches well the intuitive sensation (at least mine) that unbalanced tafl games work well up to a limit of a bit more than game balance 1.50
(Fx. Copenhagen bal. +1.51, Fetlar bal. +1.41, Sea Battle 9x9 +1.55, Brandubh +1.32 and so on).

That's not as balanced as chess. But real game balance is very diffucult in an asymmetric game, and given that the asymmetry is part of the charm of this particular game ... that kind of game balance is really good enough.I think if a variant of hnefatafl or any tafl game is too balanced, it does begin to lose some of its charm.

This is an interesting view! Perhaps part of the explanation, why the Copenhagen Hnefatafl (game balance +1.51) functions so well?

This is a very interesting statistic. I would prefer this method of tiebreaker (opponents playing two additional games), opposed to tiebreakers like game length or pieces captured.
...
If players split games in two consecutive rounds (the round robin round and the addition tiebreaker round, no previous rounds), winning all games as either black or white, then perhaps we could use tiebreakers of game length or pieces captured to determine a winner. Although I am opposed to such tiebreakers, I understand this is the real world and players can potentially continue to split games. So, such tiebreakers could at least be a means to find a winner. Anyways, the need for an extra tiebreaker round has been rare to this point.

I think for sure we should not go past a third round to determine a tournament champion. Depending on the players playing pace, the games could potentially last for months.
...
I just prefer playing games not having to worry about game length, pieces captured, or if you lost a game to a weak or strong opponent.

When it became clear that extra rounds were necessary this year in the Championship tournament, the umpire Adam and I had a talk about it. Here's an extract of the emails to show our considerations:

Adam
After several unlikely events this year, perhaps we should prepare for the eventuality that the players will tie the playoff on both points and rating?

We should consider comparing number of pieces taken (adding white and black pieces from the round as a whole for both players). This would most likely solve the issue.

Hagbard
Now where there are only two players left, who naturally are very equal in strength, I fear a bit that they will continue to tie round after round, but we'll see. As we know, Bobby Fischer and Boris Spassky had to play 21 games on Iceland in 1972, before the duel was determined...

I think you're on to something regarding more criteria to avoid rematch. Besides captured pieces there's also such a thing as game length.

I would look for numbers, which indicate elegant play. A player who fx. goes right in and wins in few moves, perhaps even without capturing any pieces, is a tafl genious (or else his opponent made a giant blunder).

[... counting ...]

So, short game length as a criterion seems to give a reasonable result.

(Number of captured pieces is open to cheating by drawing out the game so as to capture as many pieces as possible. Short game length cannot be cheated; the effective and elegant player wins the fastest.)

Adam
I like your idea of awarding for game economy, an excellent decider.

Hagbard
Or else we could find ourselves waiting for 21 games like Fischer/Spassky.

Adam
I suppose we could let them play forever, until one of them gets better at playing white?

It is an interesting conundrum though. Two players who have advanced equally as black above the rest, locked in a final until one discovers a new tactic for white.

After the Championship was determined by 3rd round without use of additional tie rules:

Hagbard
It was very lucky and the right thing that a Round 3 was
allowed instead of stopping the top final with a game length rule, which it
could've been if it was invented before the tournament.

(This I wrote because the 3rd round games were very interesting and high quality).

It is important that the fair Championship winner is found - the fair winner independent of the tournament rules.

So my bid for a conclusion is:
Game length and count of captured pieces can be auxiliary rules to rank tournament results when they are otherwise identical.
(Fx. this year bigwurm91 and Hagbard end on a split number 7 and are thus both Masters of Asgarthr 2017. With the auxiliary rules, the Master is only bigwurm91.)But they cannot be used to determine who goes to the top final or who wins the top final.
For 3rd round there are two possibilities:
- either new rounds continue until one wins, perhaps because he in the process invents new and better strategies.
- or the tournament could end with round 3, using the two auxiliary rules to spare the players' time.

Interesting. Even if you take out the Copenhagen games (which may be high due to World Championship etc), the 11x11 board is the clear favourite size. I think perhaps because a bigger board in general makes for a longer game with more strategy options, but too big a board becomes unamanagable, and games can be too long.